具有多项差分算子的三阶q-差分方程边值问题  

Boundary Value Problem of Third-order q-Difference Equations with Multi-term q-Difference Operators

作　　者：杨小辉[1] 李杰民 

机构地区：[1]广东警官学院计算机系,广东广州510230 [2]岭南师范学院数学与计算科学学院,广东湛江524048

出　　处：《四川师范大学学报（自然科学版）》2015年第6期875-883,共9页Journal of Sichuan Normal University（Natural Science）

基　　金：公安部应用创新项目(2013YYCXGDST015)

摘　　要：q-差分方程边值问题解的存在性已经引起国内外数学工作者的研究兴趣,并且得到许多有价值的结果.研究一类三阶q-差分方程边值问题,该问题是由一个三阶q-差分方程和3个具有多项q-差分算子为边界条件构成.这种边界条件可以看成是Sturm-Liouville边界条件的推广.利用Banach压缩映射原理和Krasnoselskii不动点定理,获得了该类边值问题解的存在性和唯一性的充分条件.所得条件简洁,便于验证.结果推广和改进了已有文献中的定理.最后,举2个例子来演示所得结论的应用.In recent years, an increasing interest in studying the existence of solutions for boundary value problems of q-difference equations has been observed by the domestic and foreign mathematics workers. And many valuable resuhs have been obtained. In this thesis, a class of third-order q-difference equations with boundary value conditions is concerned. The boundary value problem is consti- tuted of a third-order q-difference equation and three boundary conditions containing multi-term q-difference operators. The conditions can be regarded as extension to Sturm-Liouville boundary conditions. By using Banach＇ s contraction mapping principle and Krasnosel- skii＇ fixed point theorem, sufficient conditions for the existence and uniqueness of solutions of this problem are established. The present conditions are concise and are verified easily. The conclusions in this paper essentially extend and improve known resuhs in references. Finally, two examples are given to demonstrate the use of the main result in this paper.

关 键 词：q-差分方程 q-微分 q-积分 边值问题 

分 类 号：O175.7[理学—数学]